The Polynomials of Prime Virtual Knots of Genus 1 and Complexity at Most 5

The Polynomials of Prime Virtual Knots of Genus 1 and Complexity at Most 5 Full article

Journal

Siberian Mathematical Journal
ISSN: 0037-4466 , E-ISSN: 1573-9260

Output data

Year: 2020, Volume: 61, Number: 6, Pages: 994-1001 Pages count : 8 DOI: 10.1134/S003744662006004X

Tags

515.162.8; affine index polynomial; knot in a thickened torus; virtual knot

Authors

Vesnin A.Y. ^1,2,3 , Ivanov M.E. ¹

Affiliations

1	Laboratory of Topology and Dynamics, Novosibirsk State University, Novosibirsk, Russian Federation
2	Sobolev Institute of Mathematics, Novosibirsk, Russian Federation
3	Tomsk, Russian Federation

Akimova and Matveev classified the prime virtual knots of genus 1 which admit diagrams with at most 5 classicalcrossings in 2017. In 2018,Kaur, Prabhakar, and Vesnin introduced the families of the $ L $- and$ F $-polynomials of virtual knots generalizing the Kauffman affine index polynomial.We introduce the notion of a totally flat-trivial virtual knot. We provethat the $ L $- and $ F $-polynomials for these knots coincide with the affine indexpolynomial. Also, we establish that all Akimova–Matveev knots are totally flat-trivialand calculate their affine index polynomials. © 2020, Pleiades Publishing, Ltd.

Vesnin A.Y. , Ivanov M.E.
The Polynomials of Prime Virtual Knots of Genus 1 and Complexity at Most 5
Siberian Mathematical Journal. 2020. V.61. N6. P.994-1001. DOI: 10.1134/S003744662006004X WOS Scopus OpenAlex

Web of science:	WOS:000608907600004
Scopus:	2-s2.0-85100134133
OpenAlex:	W3111011896

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Scopus	1
OpenAlex	1
Web of science	1